Biblio

An auction-based game is formulated for coordinating the charging of a population of electric vehicles (EVs) over a finite horizon. The proposed auction requires individual EVs to submit bid profiles that have dimension equal to two times the number of time-steps in the horizon. They compete for energy allocation at each time-step. Use of the progressive second price (PSP) auction mechanism ensures that incentive compatibility holds for the auction game. However, due to cross-elasticity between the charging time-steps, the marginal valuation of an individual EV at a particular time is determined by both the demand at that time and the total demand over the entire horizon. This difficulty is addressed by partitioning the allowable set of bid profiles according to the total desired energy over the entire horizon. It is shown that the efficient bid profile over the charging horizon is a Nash equilibrium of the underlying auction game. A dynamic update mechanism for the auction game is designed. A numerical example demonstrates that the auction system converges to the efficient Nash equilibrium.

A novel class of auction-based games is formulated to study coordination problems arising from charging a population of electric vehicles (EVs) over a finite horizon. To compete for energy allocation over the horizon, each individual EV submits a multidimensional bid, with the dimension equal to two times the number of time-steps in the horizon. Use of the progressive second price (PSP) auction mechanism ensures that incentive compatibility holds for the auction games. However, due to the cross elasticity of EVs over the charging horizon, the marginal valuation of an individual EV at a particular time is determined by both the demand at that time and the total demand over the entire horizon. This difficulty is addressed by partitioning the allowable set of bid profiles based on the total desired energy over the entire horizon. It is shown that the efficient bid profile over the charging horizon is a Nash equilibrium of the underlying auction game. An update mechanism for the auction game is designed. A numerical example demonstrates that the auction process converges to an efficient Nash equilibrium. The auction-based charging coordination scheme is adapted to a receding horizon formulation to account for disturbances and forecast uncertainty.

As the population of electric vehicles (EVs) grows, coordinating their charging over a finite time horizon will become increasingly important. Recent work established a framework for EV charging coordination where a central node broadcast a price signal that facilitated the tradeoff between the total generation cost and local costs associated with battery degradation and distribution network overloading. This paper considers a completely distributed protocol where the central node is eliminated. Instead, a consensus algorithm is used to fully distribute the price update mechanism. Each EV computes a local price through its estimate of the total EV charging demand, and exchanges this information with its neighbours. A consensus algorithm establishes the average over all the EV-based prices. It is shown that under a reasonable assumption, the price update mechanism is a Krasnoselskij iteration, and this iteration is guaranteed to converge to a fixed point. Furthermore, this iterative process converges to the unique and efficient solution.